The US is similar to other countries in that family members usually care for their elderly relatives. The primary difference is there are more tools to do that with in the US.
Most elderly prefer to live independent as long as possible, but need more and more help. Eventually, in home care becomes a major burden.
My mother cares for my dad (who suffers from Parkinson's). They have enough money to make the house livable (special bed, an electric recliner chair that tilts to make it easier to exit/sit, rails in the shower, etc), but he's reached a point where he can't be left alone for longer than short periods. She can barely go to the store for groceries, let alone have any life outside the home.
A friend of mine moved her mother into her house (and rents out her mother's house). Her mother deeply resents her for that and still insists she'll eventually move back into her own house. Her mother's mental faculties are declining. My friend finally had to take away her mother's access to her own money because she kept bouncing checks. Her mother's response was to call social services and report her daughter for elderly abuse.
At least there are homes where the elderly can live and receive assistance once the level of care is beyond what the family is capable of. The quality of the homes depend on how much you can pay. If you've saved for your retirement, assisted living can be a very good experience. For the poor, Medicare and Medicaid will pay for assisted living once
all of a person's assets have been depleted. There's regulations on how elderly have to be taken care of, but the quality still varies.
Plus there are in-between options. A person can get home care on at least a part time basis, even if only to give the primary caregiver family member a much needed break.
Lastly, an aging person could commit some kind of white collar crime that would get them incarcerated for a number of years - preferably, a white collar crime that would land them in federal prison instead of state prison (quality of state prisons varies greatly among the states - there are states where a person wouldn't want to be even in a minimum security prison). Minimum security federal prisons have good medical care, constant monitoring, and the opportunity for social interaction with non-violent criminals - most of whom are of at least average intelligence. A person could even take college courses. The advantage over a home for the elderly is that residing in a federal prison is free (or almost free), so a person doesn't have to deplete all of their personal assets. (Okay, only half serious, but it really wouldn't be a horrible option.)
We talked a little bit about how to handle aging family members a few years ago (but the topic was slightly different).
https://www.physicsforums.com/threads/is-it-okay-to-cheat-on-a-spouse-that-has-alzheimers.530897